# Soft Preference Optimization: Aligning Language Models to Expert Distributions

arXiv: https://arxiv.org/abs/2405.00747 · HTML: https://mlsanity.com/paper/2405.00747/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 30 Apr 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 27 of 27)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Contrastive Preference Optimization: Pushing the Boundaries of LLM Performance in Machine Translation](https://mlsanity.com/paper/2401.08417/) (2024)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Disentangling Length from Quality in Direct Preference Optimization](https://mlsanity.com/paper/2403.19159/) (2024)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [Provably Robust DPO: Aligning Language Models with Noisy Feedback](https://mlsanity.com/paper/2403.00409/) (2024)
- [Direct Preference Optimization with an Offset](https://mlsanity.com/paper/2402.10571/) (2024)
- [Calibrating Sequence likelihood Improves Conditional Language Generation](https://mlsanity.com/paper/2210.00045/) (2022)
- [Some things are more CRINGE than others: Iterative Preference Optimization with the Pairwise Cringe Loss](https://mlsanity.com/paper/2312.16682/) (2023)
- [The Wisdom of Hindsight Makes Language Models Better Instruction Followers](https://mlsanity.com/paper/2302.05206/) (2023)
- [Unsupervised Pretraining for Sequence to Sequence Learning](https://mlsanity.com/paper/1611.02683/) (2016)
- [Relative Preference Optimization: Enhancing LLM Alignment through Contrasting Responses across Identical and Diverse Prompts](https://mlsanity.com/paper/2402.10958/) (2024)

## Built on by (most cited first, 9 of 9)

- [A Survey of Direct Preference Optimization](https://mlsanity.com/paper/2503.11701/) (2025)
- [KL-Regularized RLHF with Multiple Reference Models: Exact Solutions and Sample Complexity](https://mlsanity.com/paper/2502.01203/) (2025)
- [Deltaynamics: Language-Based Representation for Inferring Rigid-Body Dynamics From Videos](https://mlsanity.com/paper/2605.20576/) (2026)
- [C2-DPO: Constrained Controlled Direct Preference Optimization](https://mlsanity.com/paper/2502.17507/) (2025)
- [Listwise Direct Preference Optimization with Multi-Dimensional Preference Mixing](https://mlsanity.com/paper/2506.19780/) (2025)
- [Fusing Rewards and Preferences in Reinforcement Learning](https://mlsanity.com/paper/2508.11363/) (2025)
- [Exploration-Driven Optimization for Test-Time Large Language Model Reasoning](https://mlsanity.com/paper/2605.09853/) (2026)
- [Uncertainty-Normalized Margins for Direct Preference Optimization](https://mlsanity.com/paper/2609.38647/) (2026)
- [Robust Nash Alignment under Preference Uncertainty](https://mlsanity.com/paper/2610.00715/) (2026)

## Abstract (arXiv)

We propose Soft Preference Optimization (SPO), a method for aligning generative models, such as Large Language Models (LLMs), with human preferences, without the need for a reward model. SPO optimizes model outputs directly over a preference dataset through a natural loss function that integrates preference loss with a regularization term across the model's entire output distribution rather than limiting it to the preference dataset. Although SPO does not require the assumption of an existing underlying reward model, we demonstrate that, under the Bradley-Terry (BT) model assumption, it converges to a softmax of scaled rewards, with the distribution's "softness" adjustable via the softmax exponent, an algorithm parameter. We showcase SPO's methodology, its theoretical foundation, and its comparative advantages in simplicity, computational efficiency, and alignment precision.